Formation of the quasi-planar B 56 boron cluster: topological path from B 12 and disk aromaticity.

Formation and stability of the B 56 boron cluster were investigated using a topological approach and the disk aromaticity model. An extensive global energy minimum search for the B 56 system which was carried out by means of the Mexican Enhanced Genetic Algorithm (MEGA) in conjunction with density functional theory computations, confirms a quasi-planar structure as its energetically most stable isomer. Such a structural motif is derived by applying a topological leapfrog operation to a B 12 form. Its high thermodynamic stability can be explained by the disk aromaticity model in which the delocalization of its π orbitals can be assigned to the levels of a particle in a circular box with the [(1σ) 2 (1π) 4 (1δ) 4 (1φ) 4 (2σ) 2 (1γ) 4 (2π) 4 (2δ) 4 (1η) 4 (2φ) 4 (1θ) 2 ] electronic configuration. This π delocalization is confirmed by other delocalization indices. While the B 56 has a similar electron delocalization to that of the quasi-planar B 50 , they have opposite magnetic ring current properties because of the symmetry selection rules of their HOMO-LUMO electronic transitions. The π delocalization in the boron clusters is larger at long distances as compared to carbon clusters at similar sizes, but such a trend is reversed at shorter distances.